Question

ABC is a right triangle in which angle c =90degree and CD perpendicular to AB . If BC=a,CA=b,and CD=p, then prove that 1) cp=ab 2) 1/p square = 1/a square +1/b square

Answer 1

I have a question how cd can be a side

Answer 2

Answer:

1)compare the are of the triangle ABC using the 2 diff altitudes and bases. the areas will be equal so just equate it.

2)use Pythagoras theorem in ABC and sub the variables. one of the varibles will be c^2 so sun this with ab/p which we proved above. open the brackets keep 1/p^2 in one side and take the rest to other side and solve it.

you will get 1/p^2= a^2+b^2/a^2b^2

so take the RHS as  a^2/a^2b^2 + b^2/a^2b^2

                                 1/b^2+1/a^2

                                therefore 1/p^2=1/b^2+1/a^2

Step-by-step explanation: